Stochastic processes
Graduate · Statistics
Syllabus focus
Theoretical / proof-based
Pricing
Graduate-level rates are set on consultation. See the pricing page for K–12 and undergraduate rates.
Topics typically covered
Theoretical / proof-based
Markov chains
- Discrete-time Markov chains: classification of states
- Stationary distributions and ergodicity
- Continuous-time Markov chains
- Birth–death and queueing models
- MCMC as Markov chains
Poisson and renewal processes
- Poisson process: definitions and properties
- Compound Poisson processes
- Renewal theory (introduction)
- Martingales: optional stopping (intro)
- Brownian motion and diffusion (overview)
Applications to statistics
- Hidden Markov models (introduction)
- Stochastic differential equations (overview)
- Spatial point processes (preview)
- Simulation of stochastic processes
Notes
Graduate probability course oriented toward statistics students. Covers Markov chains, Poisson processes, and martingales at varying depths.